Formal properties of interpersonal envy (Q1082229)

It is well known that utility without interpersonal comparison cannot help in determining relative welfare positions of individuals. The present paper studies ''envy'' as a method to describe comparisons. The problem is studied within the framework of a general equilibrium in a market: individuals choose a utility maximizing bundle of commodities from a budget set, determined by the prices of the commodities and the income of the individual. ''Individual i envies individual j'' means that i prefers the commodity bundle chosen by j, to his own bundle. This seems to be typically an economist's view (due to Foley) on the concept of envy. Some alternative interpretations of ''envy'' in the literature are discussed. It is shown that with the help of the concept of envy agents in a market in equilibrium can be (weakly) ordered and that the ordering is complete, asymmetric and acyclic (but not necessarily transitive). It is also shown that the individual with the highest income does not envy anybody, whereas the individual with lowest income is not envied by anybody. At equal incomes the economy is envy-free, but envy-freeness does not imply equality. So the order generated by the envy relation is strongly related to incomes.